We have the system of equations:

1. $-3x - 3y = 3$
2. $y = -5x - 17$

To solve for $x$ and $y$, let's substitute the expression for $y$ from the second equation into the first equation.

From equation 2, $y = -5x - 17$. Now, substitute this into equation 1:

$-3x - 3(-5x - 17) = 3$

Now simplify:

$-3x + 15x + 51 = 3$

Combine like terms:

$12x + 51 = 3$

Now, isolate $x$:

$12x = 3 - 51$ $12x = -48$ $x = \frac{-48}{12}$ $x = -4$

Now that we have $x = -4$, substitute this value back into equation 2 to find $y$:

$y = -5(-4) - 17$ $y = 20 - 17$ $y = 3$

Solution:

The solution to the system is $x = -4$ and $y = 3$.

Would you like a detailed explanation of any of the steps or any further clarification?

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Here are some related questions you might find interesting:

1. How can you check if the solution is correct by substituting $x = -4$ and $y = 3$ into the original equations?
2. How do you solve systems of equations using substitution or elimination?
3. What would happen if the system of equations had no solution?
4. What is the graphical representation of this system of equations?
5. How would the solution change if the coefficients of $x$ and $y$ in the equations were different?

Tip: When solving systems of equations, substitution is an effective method when one of the equations is already solved for one variable, as it allows you to quickly find the other variable.